The goal of rock physics analysis is to explore relationships between geophysical observations and physical properties in earth materials. Historically, rock physics theory and empirical relationships have been used to constrain porosity estimates, leading to improved reservoir, environmental, and geotechnical characterizations. In this paper, we discuss three total porosity domains, each with differing physical, hydraulic, elastic, and electrical properties. These porosity domains are separated by the system's porous percolation threshold and critical porosity, both of which can be estimated using percolation theory.

Percolation thresholds and porosity types

Picture a simple system of, let's say, saturated grains that have been sufficiently cemented so that the pores have reached a point of isolation and disconnection (Figure 1a); in other words, the pores are “suspended” in the granular medium. Now, picture a saturated system of grains so loose that the grains are suspended in the saturating fluid (Figure 1b); in other words, the grains are isolated and disconnected.

The first system is at its porous percolation threshold (i.e., the pores no longer percolate) and the second is at its granular percolation threshold, also known as critical porosity (i.e., the grains no longer “percolate”; they are disconnected). Percolation theory defines the threshold at which randomly oriented ellipsoids, whether pores or grains, are no longer connected. The porous and granular percolation thresholds can …